Damped Sinusoids Research Articles

Increasing the efficiency and efficacy of second-order blind identification (SOBI) methods

This paper proposes a new technique to increase the efficiency and effectiveness of second-order blind identification (SOBI) methods by reducing the number of time-lagged covariance matrices required to produce highly accurate mixing matrix estimates. The technique is based on randomly selecting the time-lagged covariance matrices as opposed to choosing them sequentially, which takes advantage of a property of independence with regard to the selection of time-lagged covariance matrices, while simultaneously reducing the correlation between selected covariance matrices. The proposed randomized approach is first applied to undamped and damped sinusoids to demonstrate its effectiveness. The randomized method is then applied to a three-degree-of-freedom linear structure subjected to random excitation. Finally, the proposed method is incorporated into a modified version of the SOBI method and applied to perform identification of the UCLA Factor building from recorded earthquake responses. In each case, the performance of the randomized approach is compared with the traditional sequential selection of time-lagged covariance matrices, and the randomized approach consistently demonstrates superior performance both in terms of accuracy and efficiency. Additionally, the proposed randomized SOBI approach was easily inserted into the modified SOBI method demonstrating its malleability for SOBI variants and other blind source separation methods. Copyright © 2016 John Wiley & Sons, Ltd.

A trigger generator for controlling a high-current triggered vacuum switch

A trigger generator (TG) with a discharge of a storage capacitor through the trigger gap of a triggered vacuum switch (TVS) was developed. It provides a voltage amplitude of up to 7 kV across the trigger gap. After a gap breakdown, the TG provides an ignition current in the form of a damped sinusoid with an amplitude of ≥1 kA. It differs from analogous devices by pulsed charging of the storage capacitor and the use of an output self-breakdown gas-filled switch. The developed design of the gas switch with gas preionization in the spark gap by an additional corona discharge provides high stability of both the pulsed-breakdown voltage and the switching-on time. The TG tests showed reliable and stable switching-on of high-current TVSs of different modifications with a discharge-current rise rate of up to 3 × 1010 А/s.

Stochastic shock response spectrum decomposition method based on probabilistic definitions of temporal peak acceleration, spectral energy, and phase lag distributions of mechanical impact pyrotechnic shock test data

Most of the times pyrotechnic shock design and test requirements for space systems are provided in Shock Response Spectrum (SRS) without the input time history. Since the SRS does not describe the input or the environment, a decomposition method is used to obtain the source time history. The main objective of this paper is to develop a decomposition method producing input time histories that can satisfy the SRS requirement based on the pyrotechnic shock test data measured from a mechanical impact test apparatus. At the heart of this decomposition method is the statistical representation of the pyrotechnic shock test data measured from the MIT Lincoln Laboratory (LL) designed Universal Pyrotechnic Shock Simulator (UPSS). Each pyrotechnic shock test data measured at the interface of a test unit has been analyzed to produce the temporal peak acceleration, Root Mean Square (RMS) acceleration, and the phase lag at each band center frequency. Maximum SRS of each filtered time history has been calculated to produce a relationship between the input and the response. Two new definitions are proposed as a result. The Peak Ratio (PR) is defined as the ratio between the maximum SRS and the temporal peak acceleration at each band center frequency. The ratio between the maximum SRS and the RMS acceleration is defined as the Energy Ratio (ER) at each band center frequency. Phase lag is estimated based on the time delay between the temporal peak acceleration at each band center frequency and the peak acceleration at the lowest band center frequency. This stochastic process has been applied to more than one hundred pyrotechnic shock test data to produce probabilistic definitions of the PR, ER, and the phase lag. The SRS is decomposed at each band center frequency using damped sinusoids with the PR and the decays obtained by matching the ER of the damped sinusoids to the ER of the test data. The final step in this stochastic SRS decomposition process is the Monte Carlo (MC) simulation. The MC simulation identifies combinations of the PR and decays that can meet the SRS requirement at each band center frequency. Decomposed input time histories are produced by summing the converged damped sinusoids with the MC simulation of the phase lag distribution.

Tunable Magnetization Dynamics in Interfacially Modified Ni81Fe19/Pt Bilayer Thin Film Microstructures.

Interface modification for control of ultrafast magnetic properties using low-dose focused ion beam irradiation is demonstrated for bilayers of two technologically important materials: Ni81Fe19 and Pt. Magnetization dynamics were studied using an all-optical time-resolved magneto-optical Kerr microscopy method. Magnetization relaxation, precession, damping and the spatial coherence of magnetization dynamics were studied. Magnetization precession was fitted with a single-mode damped sinusoid to extract the Gilbert damping parameter. A systematic study of the damping parameter and frequency as a function of irradiation dose varying from 0 to 3.3 pC/μm2 shows a complex dependence upon ion beam dose. This is interpreted in terms of both intrinsic effects and extrinsic two-magnon scattering effects resulting from the expansion of the interfacial region and the creation of a compositionally graded alloy. The results suggest a new direction for the control of precessional magnetization dynamics, and open the opportunity to optimize high-speed magnetic devices.

Transmission characteristics of a TEM waveguide for transient signals by the use of a damped sinusoidal

Abstract. This article broaches the issue of the propagation of transient signals in gigahertz transverse electromagnetic (GTEM) cells. As a representative for transient signals a damped sinusoidal (DS) is used with three different mid-band frequencies. The signal transmission of the DS in the GTEM1250 is qualified and discussed on the basis of the Pearson correlation coefficient (Pcc). The Pcc gives an overview of the signal transmission quality for all measuring points within the testvolume and signal distortions can be identified. A 100 MHz DS is weakly distorted in several measuring points. The Pcc at those points decreases and a signal shape variance can be assumed. Furthermore inhomogeneities of the GTEM1250 caused by the cell door can be identified.

Simulation Analysis of Interface Circuits for Piezoelectric Energy Harvesting with Damped Sinusoidal Signals and Random Signals

Various interface circuits for collecting the energy of piezoelectric cantilever beams have been widely investigated. Such circuits include the standard interface, series synchronized switch harvesting interface circuit, parallel synchronized switch harvesting interface, synchronized charge extraction interface, and others. Most studies focus on the performance of different interface circuits with standard sinusoidal excitations. However, in real situations where constant harmonic vibrations are not present, the equivalent voltage from piezoelectric cantilever beams with excitations is not necessarily sinusoidal. In the present study, a simulation analysis of four different interface circuits with signal sources that are both damped sinusoidal and random was performed using Matlab and PSpice. The results show that the interface circuits have improved performance under low load resistance values with damped sinusoidal signal. In addition, the parallel and series synchronized switch harvesting interface circuits may perform well in collecting piezoelectric energy with random excitations.

Echo Shaping Using Sums of Damped Complex Sinusoids

Feedback delay lines are the basis of myriad audio effects and reverberation schemes. The feedback delay line, by itself, is limited to producing an infinite sequence of exponentially decaying echoes. We introduce a new type of linear time-invariant echo effect whose impulse response is a generalized sum of damped complex sinusoids. This permits echo responses to be shaped as simple sinusoids, Fourier-based waveforms, and many other complex, possibly nonperiodic, patterns that would not be feasible with other existing methods. Additionally, because the response is complex-valued, it can be used to produce auto-panning echo effects with many kinds of spatial trajectories. The effect is computationally efficient and straightforward to implement, as it only requires a parallel combination of feedback delay lines.

Feed Signal Influence and Potential Performances of a Compact Radiation Source Based on a Helical Antenna

In the class of emerging high power electromagnetic sources, a complete pulsed power source, named MOUNA (French acronym of “Module Oscillant Utilisant une Nouvelle Architecture”) has been developed. This device must transmit waveforms with a wide frequency band and a high figure-of-merit. To improve the overall performance of the MOUNA system while maintaining its compact size, two approaches are being explored in the paper: the replacement of the dipole antenna by a helical antenna and its feeding signal influence. Helical antenna is cylindrical shape and relatively compact. It offers relatively good gain factor and directivity. The waveform delivered to the antenna is directly related to the amplitude of the radiated electric field. Therefore, different waveforms (step pulse, Gaussian pulse, bipolar pulse and damped sinusoid) are compared to point out the feed signal influence on the radiated electric field. Switch oscillators appear to be considered as interesting resonant sources for driving an antenna. The novel radiating source consists of a primary power source, a resonant transformer, a coaxial transmission line damped oscillator (also termed as coaxial resonator), and a helical antenna. This high voltage pulsed source is very compact (volume of only 2500 cc without the antenna). Our study aims at designing the antenna (number of turns, size…) and a coaxial damped oscillator directly implemented at the output of the transformer. A CST-based simulation is proposed to predict the performances of this wideband source.

An improved performance frequency estimation algorithm for passive wireless SAW resonant sensors.

Passive wireless surface acoustic wave (SAW) resonant sensors are suitable for applications in harsh environments. The traditional SAW resonant sensor system requires, however, Fourier transformation (FT) which has a resolution restriction and decreases the accuracy. In order to improve the accuracy and resolution of the measurement, the singular value decomposition (SVD)-based frequency estimation algorithm is applied for wireless SAW resonant sensor responses, which is a combination of a single tone undamped and damped sinusoid signal with the same frequency. Compared with the FT algorithm, the accuracy and the resolution of the method used in the self-developed wireless SAW resonant sensor system are validated.

Stochastic algorithms for solving structured low-rank matrix approximation problems

In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. We demonstrate that finding optimal solutions of this problem is very hard. For example, we argue that if HSLRA is considered as a problem of estimating parameters of damped sinusoids, then the associated optimization problem is basically unsolvable. We discuss what is known as the orthogonality condition, which solutions to the HSLRA problem should satisfy, and describe how any approximation may be corrected to achieve this orthogonality. Unlike many other methods described in the literature the family of algorithms we propose has the property of guaranteed convergence.

An Interpolation Algorithm for Discrete Fourier Transforms of Weighted Damped Sinusoidal Signals

An algorithm for improving the accuracy of the estimation of parameters that characterize a multifrequency damped sinusoidal signal is presented. The core ideas of the algorithm is that the signal is weighted using Hann window before discrete Fourier transform and the frequencies, amplitudes, phases, and damping factors of the signal are obtained by frequency domain interpolation. It is shown that the purpose of improving the accuracy of parameter estimation is achieved using Hann window, which reduces long-range leakage and frequency-domain interpolation that eliminates the effect of the picket fence. The sensitivity analysis of the changing of the signal parameters, noise and spectral resolution, shows that both the effects of strong noise and spectral interference are considered, proving the reliability and high-accuracy parameters estimation in a number of engineering applications. Otherwise, the characteristic of efficiency computational and low memory demands are advantageously adopted for the poor computing resources situations. Extracting the impact signal of the rotor test bed using this method is illustrated. The result shows that the method can be an optional method for the fault features extraction of the mechanical impact.

Search for gravitational wave ringdowns from perturbed intermediate mass black holes in LIGO-Virgo data from 2005–2010

We report results from a search for gravitational waves produced by perturbed intermediate mass black holes (IMBH) in data collected by LIGO and Virgo between 2005 and 2010. The search was sensitive to astrophysical sources that produced damped sinusoid gravitational wave signals, also known as ringdowns, with frequency $50\le f_{0}/\mathrm{Hz} \le 2000$ and decay timescale $0.0001\lesssim \tau/\mathrm{s} \lesssim 0.1$ characteristic of those produced in mergers of IMBH pairs. No significant gravitational wave candidate was detected. We report upper limits on the astrophysical coalescence rates of IMBHs with total binary mass $50 \le M/\mathrm{M}_\odot \le 450$ and component mass ratios of either 1:1 or 4:1. For systems with total mass $100 \le M/\mathrm{M}_\odot \le 150$, we report a 90%-confidence upper limit on the rate of binary IMBH mergers with non-spinning and equal mass components of $6.9\times10^{-8}\,$Mpc$^{-3}$yr$^{-1}$. We also report a rate upper limit for ringdown waveforms from perturbed IMBHs, radiating 1% of their mass as gravitational waves in the fundamental, $\ell=m=2$, oscillation mode, that is nearly three orders of magnitude more stringent than previous results.

A Comparison of Climate Signal Trend Detection Uncertainty Analysis Methods

Abstract Two climate signal trend analysis methods are the focus of this paper. The uncertainty of trend estimate from these two methods is investigated using Monte Carlo simulation. Several theoretically and randomly generated series of white noise, first-order autoregressive and second-order autoregressive, are explored. The choice of method that is most appropriate for the time series of interest depends upon the autocorrelation structure of the series. If the structure has its autocorrelation coefficients decreased with increasing lags (i.e., an exponential decay pattern), then the method of Weatherhead et al. is adequate. If the structure exhibits a decreasing sinusoid pattern of coefficient with lags (or a damped sinusoid pattern) or a mixture of both exponential decay and damped sinusoid patterns, then the method of Leroy et al. is recommended. The two methods are then applied to the time series of monthly and globally averaged top-of-the-atmosphere (TOA) irradiances for the reflected solar shortwave and emitted longwave regions, using radiance observations made by Clouds and the Earth’s Radiant Energy System (CERES) instruments during March 2000 through June 2011. Examination of the autocorrelation structures indicates that the reflected shortwave region has an exponential decay pattern, while the longwave region has a mixture of exponential decay and damped sinusoid patterns. Therefore, it is recommended that the method of Weatherhead et al. is used for the series of reflected shortwave irradiances and that the method of Leroy et al. is used for the series of emitted longwave irradiances.

Multichannel High-Resolution NMF for Modeling Convolutive Mixtures of Non-Stationary Signals in the Time-Frequency Domain

Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies.

Improved coincident and coherent detection statistics for searches for gravitational wave ringdown signals

We study an improved method for detecting gravitational wave (GW) signals from perturbed black holes by earth-based detectors in the quest for searching for intermediate-mass black holes (IMBHs). Such signals, called ringdowns, are damped sinusoids whose frequency and damping constant can be used to measure a black hole's mass and spin. Utilizing the output from a matched filter analysis pipeline, we present an improved statistic for the detection of a ringdown signal that is found to be coincident in multiple detectors. The statistic addresses the non-Gaussianity of the data without the use of an additional signal-based waveform consistency test. We also develop coherent network statistics to check for consistency of signal amplitudes and phases in the different detectors with their different orientations and signal arrival times. We find that the detection efficiency can be improved at least by a few tens of percent by applying these multi-detector statistics primarily because of the ineffectiveness of single-detector based discriminators of non-stationary noise, such as the chi-square test, in the case of ringdown signals studied here.

An Autoregressive Doppler Spread Estimator for Fading Channels

Doppler spread causes a significant performance degradation in fast-fading mobile communication systems. This paper proposes a novel Doppler estimation scheme that uses a damped sinusoid to approximate the autocorrelation of the fading channel. Subsequently, an Autoregressive (AR) model is used for the damped sinusoid and the parameters of the model are related to the Doppler value. The superiority of the proposed estimation method over existing state-of-the-art methods is demonstrated using numerical simulations. The proposed scheme is promising in vehicular communication systems.

The use of contact heat evoked potential stimulator (CHEPS) in magnetoencephalography for pain research

BackgroundContact heat evoked potentials (CHEP) is a thermal stimulus modality used in pain research. We examine a commercial CHEP stimulator (CHEPS) that is designed to work in an fMRI environment, but poorly understood in the MEG environment. The CHEPS attains target temperatures rapidly using sophisticated control signals that unfortunately induce artifacts in the MEG. In this paper, we summarize our experiences using the CHEPS in MEG to study pain using an experimental paradigm, and propose a novel method for managing its artifact. New methodWe introduce a novel damped sinusoid modeling (DSM) technique to remove the CHEPS artifact based on estimates of the underlying sinusoids and damping factors. We show comparisons to signal space projection (SSP) and temporal signal space separation (tSSS) methods. ResultsThe CHEPS artifact is highly dynamic, yet deterministic, switching rapidly from one frequency to another, with different spatial components. The galvanic connection between the subject and the CHEPS probe alters its performance, making pre-characterization difficult. Comparison with existing methodsSSP methods failed to remove the artifact completely. TSSS performed better than SSP; however, tSSS requires the use of a multipolar head model that decreases the dimensionality and possibly the information content of the data. In contrast, DSM offers a strictly temporal modeling approach in which the artifact is estimated as a sum of damped sinusoids which is subtracted from the data. ConclusionThough the CHEPS increases the noise floor and introduces artifacts to the data, we believe the device can be successfully used in MEG if appropriate artifact removal techniques are followed.

Parametric Modeling for Damped Sinusoids From Multiple Channels

The problem of parametric modeling for noisy damped sinusoidal signals from multiple channels is addressed. Utilizing the shift invariance property of the signal subspace, the number of distinct sinusoidal poles in the multiple channels is first determined. With the estimated number, the distinct frequencies and damping factors are then computed with the multi-channel weighted linear prediction method. The estimated sinusoidal poles are then matched to each channel according to the extreme value theory of distribution of random fields. Simulations are performed to show the performance advantages of the proposed multi-channel sinusoidal modeling methodology compared with existing methods.

Perturbation methods for the spectral analysis of a weakly nonlinear acoustic field generated by a transient insonation

In this study an infinite plane piston is considered which oscillates with finite amplitude in unbounded homogeneous fluid. To illustrate the shape of the weakly nonlinear acoustic field generated by a transient insonation, the function defined by Funch/Muller representing a damped sinusoid is used to simulate the temporal waveform of the piston vibration. The acoustic transient wave generates harmonic components as result of nonlinearities in the material properties of the fluid and in the convective terms of the propagation equation. The mathematical approach is based upon the generalized Burgers’ equation, which is a good approximation of the exact equation for the nonlinear propagation when diffraction effects are assumed to be negligible. The pressure amplitude of the fundamental is considered large enough to produce the second harmonic wave. Under the quasi-linear approximation, an analytical description of the fundamental and the second harmonic waves is elaborated. To simulate the spectrum of the weakly nonlinear acoustic field, the pressure field is written in a perturbation series where the first term is the linear acoustic field that results from an infinitesimal oscillation of the piston and the second term contains the first nonlinear contribution to the acoustic field due to the finite amplitude effects.

Location of faults generating short-duration voltage variations in distribution systems regions from records captured at one point and decomposed into damped sinusoids

This study investigates the detection and localisation of faults provoking short-duration voltage variations - sags (dips) and swells - in small power distribution networks. It aims to accomplish those tasks by capturing fault records, voltage and current waveforms, at just one point in the system, the substation. The main objective is to classify the fault type and locate the fault origin occurring in a given region of a power delivery network. For that purpose, fault inception is triggered by a sensitive phase-locked loop. Then, the captured signals are decomposed using damped sinusoids of arbitrary temporal support by means of an adaptive decomposition algorithm. Subsets of the parameters defining the damped sinusoids are used for classifying the fault type and indicating the fault location. The fault-type classification is obtained by using support vector machines, whereas the fault location is obtained by means of an artificial neural network. The simulation results for a simple but actual power distribution system with three possible places for fault occurrence are presented. The exact fault-type classifications were obtained while a correct localisation of 85- of the faults was accomplished.